Adjust the equation so the line passes through the points.

ruslelena [56]

Answer:

jim is correct, x does equal 7°. justify your answer by putting seven back into the equation. it gives you back that 180 equals 180, therefore it is correct

Step-by-step explanation:

so, all angles of a triangle have to add up to 180;

(15x) + (8x - 11) + (3x + 9) = 180

15x + 8x - 11 + 3x + 9 = 180

add your common numbers

26x - 2 = 180

add 2

26x = 182

divide 26

x = 7

put it back into the equation

15(7) + 8(7) - 11 + 3(7) + 9 = 180

180 = 180

3 0

3 years ago

Mr. Ratchett, an elderly American, was found murdered in his train compartment on the Orient Express at 7 AM. When his body was

nasty-shy [4]

Answer: Mr. Ratchett died approximately at 2AM.

Step-by-step explanation: Newton's Law of Cooling shows the cooling rate between a body and the environment, by stating that the rate is proportional to the difference in temperatures between them.

Mathematically, it is represented as:

$\frac{dQ}{dt}=\alpha.A.(T_{s}-T)$

This differential equation solved, gives the solution:

$T(t)=T_{s}+(T_{0}-T_{s})e^{-kt}$

where

$T_{s}$ is temperature of the environment

$T_{0}$ is the initial temperature of the body

k is a parameter dependent of heat transfer coefficient, heat capacity and area of the body

t is time required to change the temperature

For the murder on the Orient Express, first determine parameter k.

In 1 hour, Mr. Ratchett's body decrease 1°:

$27=22+(28-22)e^{-1k}$

$5=6e^{-k}$

$e^{-k}=\frac{5}{6}$

$ln(e^{-k})=ln(0.834)$

k = 0.1823

Using the parameter, find estimate time:

$28=22+(37-22)e^{-0.1823t}$

$6=15e^{-0.1823t}$

$ln(e^{-0.1823t})=ln(0.4)$

0.1823t = 0.9163

$t=\frac{0.9163}{0.1823}$

t ≈ 5 hours

The body was found at 7AM. So, it took approximately 5 hours to cool down to 28° at that time. Therefore, Mr. Ratchett died at 2AM.

5 0

3 years ago

What is the average rate of change if this function interval x = -3 to x = 0

jok3333 [9.3K]

The average rate of change of the function, over the given interval is 2.

This question is incomplete, the complete question is:

What is the average rate of change of f(x) = 2x+10, if this function interval are x = -3 to x = 0.

<h3>What is the average rate of change over the interval?</h3>

The average rate of change of f(x) over the interval [a,b] is expressed as;

$\frac{f(b)-f(a)}{b-a}$

Given that;

f(x) = 2x + 10
Interval: [ -3, 0 ], a = -3 and b = 0

We substitute our values into the expression above.

$\frac{f(b)-f(a)}{b-a}\\\\\frac{f(0)-f(-3)}{0-(-3)}\\\\\frac{[2(0)+10]-[2(-3)+10]}{0-(-3)}\\\\\frac{[10]-[-6+10]}{3}\\\\\frac{[10]-[4]}{3}=\frac{6}{3}=2$

Therefore, the average rate of change of the function, over the given interval is 2.

Learn more about average rate of change: brainly.com/question/23715190

#SPJ1

3 0

2 years ago

When to use 22/7 for pi?

MAVERICK [17]

You don't use it usually because teachers usually say use 3.14 as an approximation

4 0

3 years ago

{ x + y = 158 x- y = 112

ZanzabumX [31]

Answer:

i have know

Step-by-step explanation:

3 0

3 years ago